This script is the repeatable script for measuring changes in the different diversity metrics and how they are affected by the different stressors. In this section we are going to analyse the results from the optim.replicates chain
Here I'm going to display the results in box plot for each metric in each broad category. > We can probably think of a better way to display the results in the future.
For each metric displayed here:
biased metric score - random metric score) for each simulation).centred scores/max(abs(centred scores))).We centre the metric based on the null results by substracting the score of the metric from the randomly reduced trait space to the stressed trait space (i.e. \(score_{centred} = score_{stressed} - score_{random}\)). We then scale the centred metric by dividing it by it's maximum absolute centred value between all stressors (i.e. \(score_{scaled} = score_{centred} / \text{max}(|scores_{centred}|))\)).
To measure the differences between the random and stressed metric scores, we ran paired t-tests between each pairs of unscaled metric score for the random reduction of the trait space and the stressed reduction of the trait space (t.test(random_scores, stressor_scores, paired = TRUE)).
To check the trend in the different level of data removals (20, 40, 60 and 80%) using a linear model with the \(scores_{scaled}\) as a response to the different removal levels (lm(scaled_metric ~ removal_level).
| equalizing.Slope | equalizing.adj.R^2 | facilitation.Slope | facilitation.adj.R^2 | filtering.Slope | filtering.adj.R^2 | competition.Slope | competition.adj.R^2 | |
|---|---|---|---|---|---|---|---|---|
| TPD_TPD_regularity | 0.24*** | 0.637 | 0.044*** | 0.037 | 0.111*** | 0.199 | 0.018** | 0.008 |
| hypervolume_BAT_regularity | -0.001 | -0.001 | 0.004 | -0.001 | 0.064*** | 0.093 | 0.015** | 0.009 |
| dendrogram_BAT_regularity | 0 | -0.001 | 0.004*** | 0.167 | -0.003 | -0.001 | 0.002*** | 0.032 |
| dissimilarity_FD_regularity | 0.004. | 0.003 | 0.189*** | 0.87 | 0.008 | 0.001 | 0.015*** | 0.06 |
| TPD_TPD_divergence | 0.176*** | 0.618 | 0.01. | 0.003 | 0.087*** | 0.15 | 0.042*** | 0.084 |
| hypervolume_BAT_divergence | 0.105*** | 0.545 | 0.018*** | 0.038 | 0.049*** | 0.096 | 0.012*** | 0.03 |
| dendrogram_BAT_divergence | 0.09*** | 0.455 | 0.023*** | 0.113 | 0.04*** | 0.044 | 0.016*** | 0.101 |
| dissimilarity_melodicMPD_divergence(MPD) | 0.167*** | 0.895 | 0.038*** | 0.158 | 0.076*** | 0.186 | 0.032*** | 0.172 |
| dissimilarity_melodicRao_divergence(Rao) | 0.165*** | 0.903 | 0.039*** | 0.173 | 0.075*** | 0.177 | 0.032*** | 0.192 |
| dissimilarity_FD_divergence(Rao) | 0.131*** | 0.616 | 0.005 | 0.001 | 0.004 | -0.001 | 0.003 | 0 |
| dissimilarity_FD_divergence | -0.046*** | 0.074 | 0.005 | -0.001 | -0.001 | -0.001 | 0.026*** | 0.027 |
| TPD_TPD_richness | 0.084*** | 0.393 | 0.026*** | 0.085 | 0.05*** | 0.099 | 0.02*** | 0.066 |
| hypervolume_BAT_richness | 0.034*** | 0.066 | -0.001 | -0.001 | 0.017** | 0.013 | 0.004 | 0 |
| convex hull_BAT_richness | 0.042*** | 0.098 | 0.014*** | 0.015 | 0.033*** | 0.05 | 0.015*** | 0.024 |
| dendrogram_BAT_richness | 0.112*** | 0.713 | 0.062*** | 0.464 | 0.059*** | 0.092 | 0.022*** | 0.116 |
| equa.rm1 | equa.rm2 | equa.rm3 | faci.rm1 | faci.rm2 | faci.rm3 | filt.rm1 | filt.rm2 | filt.rm3 | comp.rm1 | comp.rm2 | comp.rm3 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| TPD_TPD_regularity | 0.086*** | 0.041*** | 0.008*** | 0.018*** | 0.017*** | 0.009*** | 0.054*** | 0.035*** | 0.018*** | 0.043*** | 0.037*** | 0.034*** |
| hypervolume_BAT_regularity | -0.006 | -0.004 | -0.006. | 0.007 | 0.013** | 0.009** | 0.091*** | 0.07*** | 0.057*** | 0.028*** | 0.022*** | 0.021*** |
| dendrogram_BAT_regularity | 0 | 0** | 0** | 0.002*** | 0* | 0 | 0.01*** | 0.01*** | 0.011*** | 0.001*** | 0. | 0** |
| dissimilarity_FD_regularity | -0.028*** | -0.036*** | -0.035*** | 0.255*** | 0.161*** | 0.067*** | 0.02** | 0.021*** | 0.013* | 0.028*** | 0.025*** | 0.018*** |
| TPD_TPD_divergence | 0.106*** | 0.043*** | 0.006** | -0.002 | -0.003 | -0.007** | 0.045*** | 0.006 | -0.01** | 0.046*** | 0.033*** | 0.03*** |
| hypervolume_BAT_divergence | 3.101*** | 2.413*** | 1.831*** | 0.997*** | 0.865*** | 0.729*** | 2.01*** | 1.573*** | 1.286*** | 0.728*** | 0.622*** | 0.542*** |
| dendrogram_BAT_divergence | 0.228*** | 0.151*** | 0.1*** | 0.081*** | 0.069*** | 0.053*** | 0.154*** | 0.118*** | 0.094*** | 0.064*** | 0.054*** | 0.046*** |
| dissimilarity_melodicMPD_divergence(MPD) | 0.177*** | 0.121*** | 0.083*** | 0.059*** | 0.049*** | 0.039*** | 0.109*** | 0.081*** | 0.063*** | 0.053*** | 0.041*** | 0.035*** |
| dissimilarity_melodicRao_divergence(Rao) | 0.173*** | 0.12*** | 0.082*** | 0.058*** | 0.049*** | 0.039*** | 0.108*** | 0.082*** | 0.064*** | 0.051*** | 0.041*** | 0.035*** |
| dissimilarity_FD_divergence(Rao) | 2.799*** | 2.047*** | 1.407*** | 0.887*** | 0.798*** | 0.645*** | 1.267*** | 1.137*** | 0.934*** | 0.735*** | 0.63*** | 0.536*** |
| dissimilarity_FD_divergence | -0.045*** | -0.041*** | -0.034*** | -0.006. | -0.003 | -0.006*** | -0.004 | -0.01*** | -0.004 | 0.012*** | 0.001 | 0.001 |
| TPD_TPD_richness | 68.84*** | 70.55*** | 63.552*** | 32.991*** | 34.906*** | 33.619*** | 49.634*** | 49.58*** | 46.529*** | 17.838*** | 18.872*** | 16.442*** |
| hypervolume_BAT_richness | 65.974*** | 55.474*** | 44.959*** | 30.603*** | 27.608*** | 23.517*** | 49.959*** | 40.682*** | 33.453*** | 23.359*** | 20.178*** | 17.03*** |
| convex hull_BAT_richness | 38.128*** | 43.105*** | 41.169*** | 20.963*** | 23.36*** | 23.19*** | 30.242*** | 32*** | 30.807*** | 11.358*** | 12.664*** | 11.098*** |
| dendrogram_BAT_richness | 31.477*** | 37.305*** | 34.81*** | 23.064*** | 30.805*** | 31.594*** | 24.364*** | 30.483*** | 32.403*** | 8.065*** | 11.123*** | 11.106*** |
Figure 1: Simulation results: the y axes represent the different metrics tested (sorted by categories). The different columns represent the different stressors. The x-axes represent the metric values centred on the random changes and scaled by the maximum value for each metric between the four stressors. Negative and positive values signify a decrease/increase in the metric score. The dots represent the median metric value, the full line their 50% confidence interval (CI) and the dashed line their 95% CI. The colours are just here to visually separate the metrics rows but the colour gradient within each row corresponds to a removal of respectively 80%, 60%, 40% and 20% of the data (from top to bottom). Grey lines in the background are a fitted linear model on the scaled metric score function of removal amount and the value displayed is the adjusted R^2 from each of these models. Dashed grey lines represent non-significant models (slope or/and intercept). The grey line plots represent (CI + median) represent distribution of metrics scores not clearly different from the random metric scores (paired t-test p value > 0.05).
These were our expectations:
| Mechanism | Richness | Dispersion | Regularity |
|---|---|---|---|
| Equalizing | Lower | Lower | Higher |
| Facilitation | Higher | Higher | Higher |
| Filtering (exclusion) | Higher | Higher | Higher |
| Competition | Lower | Lower | Nothing |
And these are our results per metric family:
NOTE: the difference between [ok] and [-ok] is actually not really meaningful here since these graphs shows differences compared to the null results so if both the null and stressor results increase but the stressor increases slowlier than the stressor, the results in the table will decrease. Although in general, if this is the case, this is a "bad" results since ideally we would want the null to not change at all (i.e. if the metric is just picking up changes in number of elements, this is not really useful).
| Mechanism | Richness (alpha) | Dispersion | Regularity |
|---|---|---|---|
| Equalizing | [ok] Lower | [ok] Lower | [-ok] Higher |
| Facilitation | [NO] Higher | [-ok] Higher | [-ok] Higher |
| Exclusion | [NO] Higher | [-ok] Higher | [-ok] Higher |
| Competition | [ok] Lower | [ok] Lower | [NO] Nothing |
| Mechanism | Richness (Rao) | Dispersion | Regularity |
|---|---|---|---|
| Equalizing | [NO] Lower | [ok] Lower | [-ok] Higher |
| Facilitation | [NO] Higher | [-ok] Higher | [NO] Higher |
| Exclusion | [-ok] Higher | [-ok] Higher | [-ok] Higher |
| Competition | [ok] Lower | [ok] Lower | [NO] Nothing |
| Mechanism | Richness (Rao) | Dispersion | Regularity |
|---|---|---|---|
| Equalizing | [NO] Lower | [-ok] Lower | [-ok] Higher |
| Facilitation | [-ok] Higher | [NO] Higher | [NO] Higher |
| Exclusion | [NO] Higher | [NO] Higher | [NO] Higher |
| Competition | [ok] Lower | [NO] Lower | [ok] Nothing |
| Mechanism | Richness (Rao) | Dispersion | Regularity |
|---|---|---|---|
| Equalizing | [NO] Lower | [ok] Lower | [-ok] Higher |
| Facilitation | [NO] Higher | [-ok] Higher | [-ok] Higher |
| Exclusion | [NO] Higher | [-ok] Higher | [-ok] Higher |
| Competition | [NO] Lower | [ok] Lower | [NO] Nothing |
I actually don't remember of the top of my head what the convex.hull and melodic rao/mpd are representing.
And finally below are all the correlations per stressor between each metric per removal levels (20, 40, 60, 80%).
TODO: do the PCA plots as suggested by Carlos to see things clearlier.